Evaluate the integrals in Exercises 23–26. TT 23. cos (x + y + z) dx dy dz 0 Jo Jo -In 7 cln2 cIn5 elx+y+z) dz dy dx In 4 24. In6 Jo x² px+y 25. (2x – y – z) dz dy dx 2y dy dz dx 26.

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: 1) Evaluate the integral 2) Evaluate the integral S 5 sec² t de (tant — - 1 dx 8 x√√x² 2

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Q: dx Evaluate: 1) 2) -2x 3) 4) 5) 5-y'

A: *** As per our guidelines, we are supposed to solve only the first three problems/subdivisions.…

Q: 4). 2 ava-1 3). S sech-x tanh;x dx 2 2 6). S csch* 2x dx 7). S x² sech x³ dx

A: Since  we are given with the multiple number of question and our guideline is solve first question…

Q: 1 d) ₁ √²-7 dx

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Q: f:(-2,1]→[0,12] literal and overlapping function 12 if įs(x) dx = 13andſls*(x) đx =5 [f*(x) dx=? 10

A: Given :f:-2,1→0,12 literal and overlapping function.∫-21fxdx=13     →1∫06f-1xdx=5    →2To…

Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: z = sin(6x) sin(5y) az az dy II

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Q: 6. Evaluate: cin 4 a) (4x – 3) dx c) S* 2e* dx b) L, x²(-2x³ – 3)* dx d) ƒ dx e) S,(x + 1)(x² + 2x +…

A: (6) (a)To evaluate ∫254x-3dx Solution:…

Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

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Q: Find the general solution u(x,y) of: uxy : 2y. =

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Q: classify > 0²2 8x² +4 dez 2 дуг By usin this rule B²-4AC = 0

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Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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Q: le can define an operator * : 2'(R?) n'(R?) by defining *dx = dy and *dy = -dx, and extending…

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Q: 8) Use the Trapezoidal Rule to evaluate V1+ x² dx;n = 3.

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Q: 5) What is the maximum value of y = 5 Cos 4x ?

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Q: Prove that dl = (Vu) x (Vv) - do.

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Q: Differentiate. y= In [(x+7)* x + 8)®(x +2)°] dx

A: Given y = ln(x+7)4(x+8)6(x+2)3

Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: dy then dx If y = In(x/x² + 1), 2x2 + 1 C) x/x² + 1 2a2 +1 D) x(x² + 1) x² + x +1 E) x(x² + 1) 1 A)…

A: Find the derivative

Q: TT 4 3. f(1 + sinx) dx + f(1 + sinx) dx 0 TU 4

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Q: Substitute r = 1 into + p(z)y=f(z)y and show the result is linear. Write your answer in linear…

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Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: 18. Evaluate L (s² + 1)²

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Q: dx and u = 3x-2 1. y 2+1 + 3

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Q: Differentiate. 1) f(x) = 4x2 - 5x+4 A) f'(x) = 4x-5 2) y = (2x² + 3x)² A) B) f'(x) = 4x²-5 = 8x3 +…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…